Moscow’s involvement in Iraq could mean increased competition for Washington from a Cold War enemy.

Iraq said on Saturday that its military officials were engaged in intelligence and security cooperation in Baghdad with Russia, Iran and Syria to counter the threat from the ISIS militant group, a pact that could raise concerns in Washington.

A statement from the Iraqi military’s joint operations command said the cooperation had come “with increased Russian concern about the presence of thousands of terrorists from Russia undertaking criminal acts with Daesh (ISIS).”

The move could give Moscow more sway in the Middle East. It has stepped up its military involvement in Syria in recent weeks while pressing for Damascus to be included in international efforts to fight ISIS, a demand Washington rejects.

Moscow’s involvement in Iraq could mean increased competition for Washington from a Cold War enemy as long-time enemy Iran increases its influence through Shiite militia allies just four years after the withdrawal of U.S. troops.

By raising the stakes in Syria’s four-year-old civil war, Russia has prompted its Cold War foe to expand diplomatic channels with it.

Western officials have said U.S. Secretary of State John Kerry wants to launch a new effort at the U.N. General Assembly this week to try to find a political solution to the Syrian conflict.

Diplomacy has taken on new urgency in light of Russia’s military build-up in support of Syrian President Bashar al-Assad and a refugee crisis that has spilled into Europe.

Critics have urged U.S. President Barack Obama to be more decisive in the Middle East, particularly towards the Syrian conflict, and say lack of a clear American policy has given ISIS opportunities to expand.

Russian news agency Interfax quoted a military diplomatic source in Moscow as saying the Baghdad coordination center would be led on a rotating basis by officers of the four countries, starting with Iraq.

The source added a committee might be created in Baghdad to plan military operations and control armed forces units in the fight against ISIS.

A Russian foreign ministry official told Interfax on Friday that Moscow could “theoretically” join the U.S.-led coalition against ISIS if Damascus were included in international efforts to combat ISIS and any international military operation in Syria had a U.N. mandate.

Iraqi officials on Friday had denied reports of a coordination cell in Baghdad set up by Russian, Syrian and Iranian military commanders aimed at working with Iranian-backed Shiite militias in Iraq.

The armed groups, some of which have fought alongside troops loyal to Assad, are seen as a critical weapon in Baghdad’s battle against the radical Sunni militants of ISIS.

Iraqi Foreign Minister Ibrahim al-Jaafari said in New York on Friday that his country had not received any Russian military advisers to help its forces but called for the U.S.-led coalition to bomb more ISIS targets in Iraq.

Despite more than $20 billion in U.S. aid and training, Iraq’s army has nearly collapsed twice in the last year in the face of advances by ISIS, which controls large swathes of territory in the north and west of the OPEC oil producer.